A class of Dirichlet problems for the Helmholtz equation
Bill Williams · The Quarterly Journal of Mechanics and Applied Mathematics · 1997
A formal solution is obtained to a class of Dirichlet problems for Helmholtz's equation within a corner. It is shown that, for corner angles pπ/q, where p and q are relatively prime integers, the expansions of the solutions in the neighbourhood of the corner include a term proportional to rq In (r), where r is the distance from the corner. A sufficient condition to ensure the absence of such terms is given.